Exercise 24.2
Page-24.13Question 1:
Calculate the mean for the following distribution:
| x: | 5 | 6 | 7 | 8 | 9 |
| f: | 4 | 8 | 14 | 11 | 3 |
Answer 1:
The given distribution in tabulated form is
Prepare the following frequency table of which the first column consists of the values of the variate and the second column the corresponding frequencies. Multiply the frequency of each row with the corresponding values of variable to obtain the third column containing
.
Find the sum of all entries in the second and third column to obtain N and
respectively. Therefore,
Hence the mean is
Question 2:
Find the mean of the following data:
| x: | 19 | 21 | 23 | 25 | 27 | 29 | 31 |
| f: | 13 | 15 | 16 | 18 | 16 | 15 | 13 |
Answer 2:
The given distribution in tabulated form is
Prepare the following frequency table of which the first column consists of the values of the variate and the second column the corresponding frequencies. Multiply the frequency of each row with the corresponding values of variable to obtain the third column containing.
Find the sum of all entries in the second and third column to obtain N andrespectively. Therefore,
Hence the mean is
Question 3:
Find the mean of the following distribution:
| x: | 10 | 12 | 20 | 25 | 35 |
| f: | 3 | 10 | 15 | 7 | 5 |
Answer 3:
The given distribution in tabulated form is
Prepare the following frequency table of which the first column consists of the values of the variate and the second column the corresponding frequencies. Multiply the frequency of each row with the corresponding values of variable to obtain the third column containing. Find the sum of all entries in the second and third column to obtain N andrespectively.
Find the sum of all entries in the second and third column to obtain N and respectively. Therefore,
Hence the mean is
Question 4:
Five coins were simultaneously tossed 1000 times and at each toss the number of heads were observed. The number of tosses during which 0, 1, 2, 3,4 and 5 heads were obtained are shown in the table below. Find the mean number of heads per toss.
| No. of heads per toss | No. of tosses |
| 0 1 2 3 4 5 |
38 144 342 287 164 25 |
| Total | 1000 |
Answer 4:
The given data can be tabulated in the form
The row of x denotes the number of heads per toss and the row of f denotes the number of tosses.
Prepare the following frequency table of which the first column consists of the number of heads and the second column the number of tosses (frequencies). Multiply the frequency of each row with the corresponding number of heads to obtain the third column containing.
Find the sum of all entries in the second and third column to obtain N (already given in the question) and respectively. Therefore,
Hence the mean number of heads per toss is
Question 5:
The mean of the following data is 20.6. Find the value of p.
| x: | 10 | 15 | p | 25 | 35 |
| f: | 3 | 10 | 25 | 7 | 5 |
Answer 5:
The given distribution in tabulated form is
We have to find the value of p using the information that the mean of the distribution is 20.6.
Prepare the following frequency table of which the first column consists of the values of the variate and the second column the corresponding frequencies. Multiply the frequency of each row with the corresponding values of variable to obtain the third column containing.
Find the sum of all entries in the second and third column to obtain N andrespectively. Therefore,
The mean is
Hence, we have
Question 6:
If the mean of the following data is 15, find p.
| x: | 5 | 10 | 15 | 20 | 25 |
| f: | 6 | p | 6 | 10 | 5 |
Answer 6:
The given data in tabulated form is
We have to find the value of p using the information that the mean of the data is 15.
Prepare the following frequency table of which the first column consists of the values of the variate and the second column the corresponding frequencies. Multiply the frequency of each row with the corresponding values of variable to obtain the third column containing.
Find the sum of all entries in the second and third column to obtain N andrespectively. Therefore,
The mean is
Hence, we have
Question 7:
Find the value of p for the following distribution whose mean is 16.6.
| x: | 8 | 12 | 15 | p | 20 | 25 | 30 |
| f: | 12 | 16 | 20 | 24 | 16 | 8 | 4 |
Answer 7:
The given distribution in tabulated form is
We have to find the value of p using the information that the mean of the distribution is 16.6.
Prepare the following frequency table of which the first column consists of the values of the variate and the second column the corresponding frequencies. Multiply the frequency of each row with the corresponding values of variable to obtain the third column containing.
Find the sum of all entries in the second and third column to obtain N andrespectively. Therefore,
The mean is
Hence, we have
Question 8:
Find the missing value of p for the following distribution whose mean is 12.58.
| x: | 5 | 8 | 10 | 12 | p | 20 | 25 |
| f: | 2 | 5 | 8 | 22 | 7 | 4 | 2 |
Answer 8:
The given distribution in tabulated form is
We have to find the value of p using the information that the mean of the distribution is 12.58.
Prepare the following frequency table of which the first column consists of the values of the variate and the second column the corresponding frequencies. Multiply the frequency of each row with the corresponding values of variable to obtain the third column containing.
Find the sum of all entries in the second and third column to obtain N and respectively. Therefore,
The mean is
Hence, we have
Question 9:
Find the missing frequency (p) for the following distribution whose mean is 7.68.
| x: | 3 | 5 | 7 | 9 | 11 | 13 |
| f: | 6 | 8 | 15 | p | 8 | 4 |
Answer 9:
The given distribution in tabulated form is
We have to find the value of p using the information that the mean of the distribution is 7.68.
Prepare the following frequency table of which the first column consists of the values of the variate and the second column the corresponding frequencies. Multiply the frequency of each row with the corresponding values of variable to obtain the third column containing.
Find the sum of all entries in the second and third column to obtain N and respectively. Therefore,
The mean is
Hence, we have
Question 10:
Find the value of p, if the mean of the following distribution is 20.
| x: | 15 | 17 | 19 | 20+p | 23 |
| f: | 2 | 3 | 4 | 5p | 6 |
Answer 10:
The given data in tabulated form is
We have to find the value of p using the information that the mean of the data is 20.
Prepare the following frequency table of which the first column consists of the values of the variate and the second column the corresponding frequencies. Multiply the frequency of each row with the corresponding values of variable to obtain the third column containing.
Find the sum of all entries in the second and third column to obtain N and respectively. Therefore,
The mean is
Hence, we have
If p is negative then the 4th frequency becomes negative. But frequency can’t be negative. Hence the possible value of p is 1
Question 11:
Candidates of four schools appear in a mathematics test. The data were as follows:
| Schools | No. of Candidates | Average Score |
| I II III IV |
60 48 Not available 40 |
75 80 55 50 |
If the average score of the candidates of all the four schools is 66, find the number of candidates that appeared from school III.
Answer 11:
Let the number of candidates appeared from school III is
.
Then the given data can be tabulated as
The row of x denotes the average scores and the row of f denotes the number of candidates. We have to find the value of p using the information that the average score of all the four schools is 66.
Prepare the following frequency table of which the first column consists of the average scores and the second column the number of candidate (frequencies). Multiply the frequency of each row with the corresponding average scores to obtain the third column containing.
Find the sum of all entries in the second and third column to obtain N and respectively. Therefore,
The mean is
Hence, we have
Hence the number of candidates appeared from school III is
.
Question 12:
Find the missing frequencies in the following frequency distribution if it is known that the mean of the distribution is 50.
| x: | 10 | 30 | 50 | 70 | 90 |
| f: | 17 | f1 | 32 | f2 | 19 |
Total 120.
Answer 12:
The given distribution in tabulated form is
We have to find the value of missing frequencies f1 and f2, using the information that the mean of the distribution is 50 and the total frequency is 120.
Prepare the following frequency table of which the first column consists of the values of the variate and the second column the corresponding frequencies. Multiply the frequency of each row with the corresponding values of variable to obtain the third column containing.
Find the sum of all entries in the second and third column to obtain N and respectively. Therefore,
The mean is
Hence, we have two equations
Adding them we get
Putting the value of f1 in the second equation we get
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